There are many intriguing thoughts given in this thread. It seems a likely enough place for me to post my current thoughts. I do not want to go into a lot of detail, but I do want to give an overview of my theories.
As Brian commented, I think on page 3, that Bran has the ability to affect people over space and time, that this is the main story going forward. Brandon was the first character given a chapter. That immediately followed the prologue where the supernatural conflict was introduced. I think Bran is affecting ghost. I think he’s looking for ways to also influence, John, Sansa, and Arya through their dreams. And maybe Jaime as well.
There are other influences taking place through dreams. Jojen. Robert Aaron. Euron Greyjoy. Dany. Perhaps Eddard. I think Benjamin stark was influenced by dreams as well. These influences may be Bran traveling through time or maybe Brynden Rivers. I am not sold that Blood raven, is the three eyed Crow. I think it is more likely that Bran himself is the three eyed Crow.
I think Howland Reed had dreams as well. I do not think that Howland is a green seer as his son Jojen is. I think Howland Reed has skin changing abilities.
I think Howland Reed, after being saved by Lyanna, at Harrenhal, conspired with Lyanna to defeat three knights. I believe Lyanna used her horse riding ability, that her father indulged, to ride as the mystery knight and win. I think Howland Reed used his skin changing abilities to interfere with the mounts of the three knights, thus allowing Lyanna to easily unhorse them.
Rhaegar was trying to unseat his father. Oswll Whent, and Arthur Dayne were loyal to him. He then co-opted Gerold Hightower. But Rhaegar was unable to gain the loyalty of Tywin Lannister and his schemes faltered. I think his plan from childhood was to bring about the prince that was promised (TPTWP), the three heads of the dragon, and Azor Ahai reborn. He did not want to do this for the glory of his family, but for the express purpose in defeating the Others.
I believe Eddard Stark loved and married Ashara Dayne. I believe Jon Snow is their son. Eddard honored the men in his life by naming his sons after them. Robb was named for his best friend. Bran was named for his murdered brother.Rickon was named for his murdered father. Naming Jon, a *******, after his foster father does not make sense. Naming Jon, his first true, born son, by Ashara Dayne, to honor his foster father, makes a great deal of sense.
I believe the mad king raped Lyanna, and Aegon is the result. In fact, I think that Aerys II had seven children. In birth order, they are Rhaegar, Cersei (Caersei), Jaime (Jaeme), Tyrion (Taerion), Viserys, Aegon, and Daenerys. This changes Jaime’s kingslaying to kinslaying. This changes Tyrion’s patricide to murder.
I believe in order to secure their success, Jon Arryn and Eddard Stark caved in to the demands of Hoster Tully. And Jon was conceived before Robb. I think Jon was born somewhere between King’s Landing and the Tower of Joy. Maybe White Harbor. Maybe Griffin’s Roost. May be the Tower of Joy.
I believe in the fight at the tower, Hightower and Whent were slain along with five of Eddard’s companions. I believe that Howland used his skin changing ability, to affect a horse or two, to stop Arthur Dayne.
I think that Eddard, Ashara, Howland, and Arthur plotted to save Rhaegar’s son, and fulfill his plan to stop the others. And Eddard sent Jon to Winterfell. Ashara and Arthur took Aegon to Essos. And Eddard sent Jeor Mormont to the Wall for supporting the Targaryens. Benjen went to the wall either as punishment for keeping Leona‘s secret or in order to be part of Rhaegar’s plans.
I believe Oberyn went to Kings Landing to further Dorans plot to strip Tywin of everything, and then murder him. I think Littleinger and Olenna were going to murder Joffrey with the wine, but Oberyn beat them to it with the cream sauce on the pie. Joffrey was not Oberyn’s target, Tyrion was. I think Shae is Sarella Sand, Oberyn‘s daughter. I think she gave Tywin the Tears of Lys on Oberyn’s orders. I think she was also going to poison Cersei, Jaime, and Tommen in accordance with Oberyn’s wishes.